3 If f(x)=3/x-3, find using technology. ____ Use this to find the equation of the tangent line to the curve y=3/x-3 at the point (5, 1.5). The equation of 2 3 this tangent line can be written in the form y = mx + b where m is: and where b is:

Answer:

Where are the statements?

Step-by-step explanation:

The expected value and variance of the sum of the numbers that come up when rolling a pair of fair dodecahedral dice are both equal to 13.

For a pair of fair dodecahedral dice, each die has 12 sides numbered from 1 to 12. The probability of getting any number from 1 to 12 on a single roll is 1/12, as each side is equally likely. Since there are two dice being rolled, the total number of possible outcomes is 12 x 12 = 144.

The expected value, denoted as E(X), is the sum of all possible outcomes multiplied by their respective probabilities. In this case, the sum of all possible outcomes is 2 to 24 (1+1, 1+2, …, 12+12), and each outcome has a probability of 1/144 (1/12 x 1/12) since the rolls are independent. Therefore, the expected value is:

E(X) = 2 x 1/144 + 3 x 1/144 + … + 24 x 1/144

Simplifying the expression, we get:

E(X) = (2 + 3 + … + 24) x 1/144

The sum of all numbers from 2 to 24 is 300, so we can substitute that into the equation:

E(X) = 300 x 1/144

E(X) = 2.08 (rounded to two decimal places)

The variance, denoted as Var(X), is a measure of how much the values of a random variable (in this case, the sum of the numbers rolled) vary around the expected value. The variance is calculated as the sum of the squared differences between each possible outcome and the expected value, multiplied by their respective probabilities.

Var(X) = [(2 - E(X))² x 1/144 + (3 - E(X))² x 1/144 + … + (24 - E(X))² x 1/144]

Substituting the calculated value of E(X) into the equation, we get:

Var(X) = [(2 - 2.08)² x 1/144 + (3 - 2.08)² x 1/144 + … + (24 - 2.08)² x 1/144]

Simplifying the expression, we get:

Var(X) = 61.73

Therefore, the expected value and variance of the sum of the numbers that come up when rolling a pair of fair dodecahedral dice are both equal to 13.

To learn more about variance here:

brainly.com/question/29505178#

#SPJ11

Answer:

\(\frac{2}{6} =\frac{6}{18}\)

Step-by-step explanation:

Compare the denominators. Since  6 ⋅ 3 = 18 , multiply the numerator  2  by  3  to get  6

The percentage of category shelf facings for Brand F is 10% out of the total facings allotted for all brands in that category, based on the information provided.

To calculate the percentage of category shelf facings for Brand F, we need to determine the proportion of shelf facings allotted to Brand F out of the total facings allotted for all brands in that category.
Company U has 100 outlets, and half of those outlets carry Brand F. This means that there are 50 outlets that carry Brand F.
Out of the 50 facings allotted for all brands in that category, Company U allots Brand F 5 shelf facings.
To find the percentage, we divide the facings allotted to Brand F (5) by the total facings allotted for all brands in the category (50), and then multiply by 100 to express it as a percentage.
(5 facings / 50 facings) * 100 = 10%
Therefore, the percentage of category shelf facings for Brand F is 10%. This indicates that Brand F occupies 10% of the available shelf space in the category across Company U's outlets.



learn more about percentage here

https://brainly.com/question/33098852



#SPJ11

The matrix of \(t\) relative to the basis \(b'\) is \(A' = \begin{bmatrix} -9 & 7 \\ -37 & 43 \end{bmatrix}\).

\(\textbf{To find the matrix of } t \textbf{ relative to the basis } b', \textbf{we have to follow some steps. The steps are described below:}\)

First, we have to find the images of basis vectors under the transformation \(t\). \(t(-1,1) = (-9,7)\) and \(t(1,-5) = (-37,43)\).

Represent the image vectors of the basis in the standard basis. We use these vectors as columns in the matrix of \(t\) in the basis \(b'\).

\((-9,7) = -9(1,0) + 7(0,1) = (-9,7) = -9(-1,1) + 7(1,-5)\)

\((-37,43) = -37(1,0) + 43(0,1) = (-37,43) = -37(-1,1) + 43(1,-5)\)

Hence, we can write the following equation: \(A[x]_{b'} = [x]_S\)

Where \(A[x]_{b'}\) is the main answer in the form of a matrix, and \([x]_S\) is the coordinate of \([x]_{b'}\) with respect to the standard basis.

Now, we will write the equations with the coordinates of the basis vectors of \(b'\).

\(A[1,0] = [-9, -37]\) and \(A[0,1] = [7, 43]\)

Now we will write the matrix of \(A\) as follows:

\(A = \begin{bmatrix} -9 & 7 \\ -37 & 43 \end{bmatrix}\)

Thus, the matrix of \(t\) relative to the basis \(b'\) is \(A' = \begin{bmatrix} -9 & 7 \\ -37 & 43 \end{bmatrix}\).

To know more about matrix, click here

https://brainly.com/question/29132693

#SPJ11

Answer:

for how much each kid gets

Step-by-step explanation: big brain math kid

Answer:

Step-by-step explanation:

The general solution of the differential equation \(\frac{d^2y}{dx^2} -6\frac{dy}{dx} +16y = sin x\), which was found using the method of undetermined coefficients, is \(y = C_1 e^{(3x)} cos x + C_2 e^{(3x)} sin x + (\frac{5}{87} ) \ sin x + (\frac{2}{87} ) \ cos x \).

To use the method of undetermined coefficients, we assume that the particular solution to the differential equation is of the form:
\(y_p\) = A sin x + B cos x
where A and B are constants to be determined.

We then take the first and second derivatives of this assumed solution:
\(y'_p\) = A cos x - B sin x
\(y''_p\) = -A sin x - B cos x

Substituting these into the differential equation \(\frac{d^2y}{dx^2} -6\frac{dy}{dx} +16y = sin x\), we get:
(-A sin x - B cos x) - 6(A cos x - B sin x) + 16(A sin x + B cos x) = sin x

Simplifying, we get:
(15A + 6B) sin x + (-6A + 15B) cos x = sin x

We equate the coefficients of sin x and cos x to their corresponding terms on the right-hand side, and solve for A and B:
15A + 6B = 1
-6A + 15B = 0

Solving for A and B, we get:
A = 5/87
B = 2/87

Therefore, the particular solution is:
\(y_p = (\frac{5}{87} ) \ sin x + (\frac{2}{87} ) \ cos x\)

The general solution is the sum of the particular solution and the complementary solution, which is the solution to the homogeneous differential equation:
\(\frac{d^2y}{dx^2} -6\frac{dy}{dx} +16y = sin x\)

The characteristic equation is:
r² - 6r + 16 = 0
which has roots:
r = 3 ± i√7

The complementary solution is:
\(y_c = C_1 e^{(3x)} cos x + C_2 e^{(3x)} sin x\)
where C₁ and C₂ are constants determined by the initial conditions.

Therefore, the general solution is:
\(y = y_c + y_p\)

\(y = C_1 e^{(3x)} cos x + C_2 e^{(3x)} sin x + (\frac{5}{87} ) \ sin x + (\frac{2}{87} ) \ cos x \)
where C₁ and C₂ are constants determined by the initial conditions.

Learn more about a general solution:

https://brainly.com/question/17004129

#SPJ11

Answer:

Step-by-step explanation:

↝m√p + n√p -√p

↝√p(m+n-1)

↝(m+n-1)√p = √p(m+n-1)

↝(m-n+1)√p ≠ √p(m+n-1)

↝(m-n-1)√p ≠√p(m+n-1)

hence, option 1st is correct ✓

Option A

Let's verify

\(\\ \rm\Rrightarrow (m+n-1)\sqrt{p}\)

\(\\ \rm\Rrightarrow m\sqrtp}+n\sqrt{p}-\sqrt{p}\)

Hence verified

the range is3,7,8

3,7,8

Answer:

the range is3,7,8

3,7,8

Step-by-step explanation:

Answer:

1872

Step-by-step explanation:on edge

Answer:

C) 1,872 square inches

Step-by-step explanation:

Hope this helps!

Brainliest if correct pls??

Answer:

21,4 ft

Step-by-step explanation:

We have in total -149.8 ft.

Consider also that we have 7 levels, so to know the depth of every single level we must do 149.8 divided by 7, so: 149,8:7=21,4 ft.

I hope i was useful to you

Answer:

n= -1.2

Step-by-step explanation:

I think because if you use slope equation to find the slope which is 3/5 and then you use point slop equation to find out what the equation would be. y=3/5x and then you substitue y for 18 and solve/simplify the equation to get -1.2.

The clearinghouse and research middle on servant management is now called c. The Greenleaf Center for Servant Leadership.

The middle turned into named after Robert K. Greenleaf, who first brought the idea of servant leadership in his essay "The Servant as Leader" published in 1970. The Greenleaf Center for Servant Leadership serves as a worldwide useful resource for promoting the knowledge and exercise of servant leadership.

It conducts studies, provides educational applications, and gives a platform for individuals and businesses to study and interact with servant management ideas. The middle's recognition is on nurturing moral and compassionate management that prioritizes the nicely-being and growth of individuals and the groups they serve. Through its initiatives, the Greenleaf Center pursuits to inspire and empower leaders to create a superb and impactful exchange by embracing the servant management philosophy.

To know more about servant leadership,

https://brainly.com/question/32614924

#SPJ4

The clearinghouse and research center on servant leadership is called The Greenleaf Center for Servant Leadership.

The clearinghouse and research center on servant leadership is called The Greenleaf Center for Servant Leadership. It is a nonprofit organization that was founded in 1964 by Robert K. Greenleaf. The center is dedicated to promoting the principles of servant leadership, which emphasizes serving others and putting their needs first.

The Greenleaf Center conducts research, provides resources and training, and serves as a hub for individuals and organizations interested in servant leadership.

About clearinghouse and research center here:

https://brainly.com/question/30246172

#SPJ11

An element is a pure material made up of atoms with the same amount of protons in their nuclei. The atomic number and the mass number of the element X are 92 and 238 respectively.

In chemistry, an element is a pure material made up of atoms with the same amount of protons in their nuclei. Chemical elements, unlike chemical compounds, cannot be broken down into simpler substances by any chemical process.

Let us consider, that z is the atomic no and A is the mass no of the parent element 'X'.

As per the question, X emits two successive alpha particles (²₁He) and one beta, i.e, particle and reached to daughter element (²³⁰₈₉Ac).

Now according to the question, we can write,

\(^A_ZX \overset{-\alpha}{\rightarrow}\ \ ^{A-4}_{Z-2}X\ +\ ^4_2He\ \ \overset{-\alpha}{\rightarrow}\ \ ^{A-8}_{Z-4}X\ +\ ^4_2He\ \ \overset{-\-\beta}{\rightarrow}\ \ ^{A-8}_{Z-3}X\ +\ ^0_{-1}He\)

We see, \(^A_ZX\) that after two α and one β of emission, we get the daughter element \(^{A-8}_{Z-3}X\). Again as given in the problem, the daughter element is \(^{230}_{89}AC\).

∴We can write-

\(^{A-8}_{Z-3}X=^{290}_{89}AC\)

comparing the two, we get,

Z-3=89

Z=92

A-8=230

A=238

Hence, the atomic number and the mass number of the element X is 92 and 238 respectively.

Learn more about Element:

https://brainly.com/question/13025901

Answer:

118,900,000,000,000 (1.189 × 10^14)

Step-by-step explanation:

First, assume that a cell is roughly a sphere with radius 10−³cm (. Let's compute the volume of the cell from the relation between radius and volume:

The volume V of a sphere with radius r is

V=(4π)/3 r³

where r³ and V have the same units. The volume of a cell with radius 10−³cm is therefore

V=4π³/3(10−³)3≈4.1888×10−⁹ cm³.

Next, we use the fact that the density of a cell is approximately the density of water which is 1g/cm³. Let's compute the mass of a cell from its volume and density using the definition of density:

density = mass/volume

which is equivalent to

mass = density×volume.

The mass of a cell is therefore

1 (g)/cm³×4.1888×10−⁹cm³ ≈ 4.1888×10−⁹g.

Now you know the mass of a cell, what other piece of information do you need to work out the number of cells in your body? Your mass in grams (if you know your weight in pounds, you can convert: 1 lb≈453.6 grams).

Number of cells=Your Mass/Mass of Cell

For example, the mass of a 175 lb is about 45,360 grams. We have that

‪79378g/4.1888×10−⁹g≈11.89 × 10^14

so there are approximately 1×10¹⁴=118,900,000,000,000 (1.189 × 10^14) cells in the human body!

The company owns five vans which is determined by the equation method.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

We can set up the following system of equations to represent the given information:

s + v = 12

3s + 8v = 61

where s represents the number of sedans and v represents the number of vans.

We can solve this system of equations using substitution.

First, we can solve the first equation for s:

s = 12 - v

We can substitute this expression for s in the second equation to get:

3(12 - v) + 8v = 61

Solving for v, we get:

36 - 3v + 8v = 61

Combining like terms, we get:

5v = 25

Dividing both sides by 5, we get:

v = 5

Therefore, the company owns 5 vans.

Learn more about the equations here:

brainly.com/question/29657992

#SPJ2

a. The ranges of g(x) and h(x) differ by a constant value of 1, since h(x) is simply g(x) shifted upward by 1 unit. Therefore, the range unit.

b.

Graph of g(x) = 2x + 1 and h(x) = 2x + 2 over the interval 0 < x < 5:

![Graph of g(x) over the interval 0 < x < 5 is (1, 11), while the range of h(x) is (2, 12). This confirms that the range of h(x) is equal to the range of g(x) shifted upward by 1 unit.

g(x) = 2x+1 h(x) = 2x + 2

for the domain 0 < x < 5.

These are two parallel lines where h(x) is 1 unit above g(x) Then, the range of h(x) over the given domain will have endpoints 1 unit greater.

g(0) = 2(0) + 1 g(0) = 0 + 1 g(0) = 1

Evaluating g(x) when x = 5 :

g(5) = 2(5) + 1

g(5) = 10 + 1

g(5) = 11

Then, we can graph g(x) by connecting the points (0, 1) and (5, 11).

Evaluating h(x) when x = 0 :

h(0) = 2(0) + 2 h(0) = 0 + 2 h(0) = 2

Evaluating h(x) when x = 5 :

h(5) = 2(5) + 2

h(5) = 10 + 2

h(5) = 12

Then, we can graph h(x) by connecting the points (0, 2) and (5, 12).

From the graph, the range of g(x) over the given domain is (1, 11) and of h(x) is (2,12)

Given the sequence:

7, -14, 28, -56,

To find the 7th term of the geometric sequence, use the formula below:

where,

a is the first term = 7

n is the number of terms = 7

r = common ratio =

Thus, we have:

The 7th term is -448

ANSWER:

A) -448

Answer:

i think its 15 gallons of water if you do the math you can see it

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

When 2 angles are congruent and corresponding, the lines are parallel

The vertex form of the equation is y = (x - 3)² - 4, which corresponds to option OD.

To convert the given equation from standard form to vertex form, we need to complete the square.

The vertex form of a parabola's equation is y = a(x-h)² + k, where (h, k) represents the vertex of the parabola.

Given equation: y = x² - 6x + 14

Move the constant term to the right side:

y - 14 = x² - 6x

Complete the square by adding and subtracting the square of half the coefficient of x:

y - 14 + 9 = x² - 6x + 9 - 9

Group the terms and factor the quadratic:

(y - 5) = (x² - 6x + 9) - 9

Rewrite the quadratic as a perfect square:

(y - 5) = (x - 3)² - 9

Simplify the equation:

y - 5 = (x - 3)² - 9

Move the constant term to the right side:

y = (x - 3)² - 9 + 5

Combine the constants:

y = (x - 3)² - 4

For similar question on vertex.

https://brainly.com/question/1217219  

#SPJ8

To duplicate angle ABC, draw a line segment, position the compass on point A, and then draw an arc that intersects the line segment. Next, position the compass on point B, and then draw a second arc that intersects the first arc at a point on the line segment. Finally, position the compass on the point where the two arcs intersect, but without changing the width, and draw a third arc that intersects the line segment.

When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.

Common instruments used to measure angles are:

1. Protractor

2.Compass

3.Digital Angle finder

4.Angle finder

5.Clinometer

6. Inclinometer

You can take the following actions to copy angle ABC:

Create a line segment that will serve as the foundation for the new angle you're going to create.

Draw an arc that crosses the line segment you produced in step 1 by positioning the compass on point A.

Draw a second arc that crosses the previous arc at a point on the line segment by setting the compass on point B.

Place the compass on the intersection of the two arcs without adjusting the compass's width, then create another arc that crosses the line segment.

Point D is where the second arc crosses the line segment. To finish the new angle, join points D and C.

To learn more about angles visit:

https://brainly.com/question/29128584

#SPJ4

In this scenario, we have a box containing 7 cameras, with 4 of them being defective. We are interested in the number of defective cameras in a sample of 2 cameras, represented by the random variable X.

To find the probability distribution for X, we calculate the chances for each possible  outgrowth. The probability of having 0  imperfect cameras( X =  0) is1/7, as there's only one way to  elect 2non-defective cameras out of the 7 available.  The anticipated value of X, denoted as E( X), provides an estimate of the average number of  imperfect cameras in a sample of 2. It's calculated by multiplying each possible  outgrowth by its corresponding probability and  casting  them up.

Probability distribution for X:

P(X = 0) = 1/7

P(X = 1) = 4/7

P(X = 2) = 2/7

Expected value of X: 1.1429

In this case, the anticipated value of X is1.1429, indicating that, on average, we'd anticipate to find  roughly1.1429  imperfect cameras in a sample of 2 cameras.   The anticipated value serves as a measure of central tendency and provides  perceptivity into the long- term average  outgrowth.

Learn more about probability distribution at

https://brainly.com/question/27992820

#SPJ4

The quarter 2 forecast for year 6 using the "quarterly seasonality without trend" model is  - a) 1992

To determine the quarter 2 forecast for year 6 using the "quarterly seasonality without trend" model, we can refer to the given Exhibit 4 data.

This model assumes that there is a repeating seasonal pattern in the sales data. Looking at the sales data for quarter 2 in each year (1056, 1156, 1301), we can observe an increasing trend.

Therefore, it is reasonable to expect that the quarter 2 forecast for year 6 would be higher than the previous year's value.

Among the options provided, the highest value is 1992, which could be the quarter 2 forecast for year 6.

learn more about forecast :
https://brainly.com/question/21445581
#SPJ4

The simple interest for a deposit of $ 5,000 at 3 % rate of interest for 1 year would be $ 150

What is Simple Interest?

Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Given data ,

Let the simple interest be represented as S

Now , the value of S is

The principal amount = $ 5,000

The rate of interest R = 3 %

The time period T = 1 year

So , the Simple Interest is given by the equation

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Substituting the values in the equation , we get

Simple Interest S = ( 5000 x 3 x 1 ) / 100

On simplifying the equation , we get

Simple Interest S = 150000 / 100

Simple Interest S = $ 150

Therefore , the value of S is $ 150

Hence , the simple interest for the deposit is $ 150

To learn more about simple interest click :

https://brainly.com/question/17282817

#SPJ2

Answer:

3.84

Step-by-step explanation:

 ((24) + 5(12) + 10(10) + 25(8)) ÷ 100 = (24 + 60 + 100 + 200) ÷ 100 Multiply.

                                                        = (384) ÷ 100                                 Add.

                                                        = 3.84                                         Divide.

The implication (p â q) is a logical statement that consists of a pair of sentences, where p represents the antecedent and q represents the consequent.

These two sentences are connected by the a operator, which means "if...then." The implication is considered true if the antecedent is true and the consequent is also true, or if the antecedent is false. However, it is false only when the antecedent is true and the consequent is false. Therefore, the truth value of the implication depends on the truth value of its two component sentences.
True, the Implication (p → q) consists of a pair of sentences separated by the → operator. In this context, p and q represent two different sentences, and the → operator signifies that if p is true, then q must also be true. This is also known as a conditional statement.

Visit here to learn more about antecedent:

brainly.com/question/24734058

#SPJ11